Final answer:
To find R^2 for the relation R = {(a, b), (b, c), (c, d)}, we identified pairs where the second element of one pair is the first element of the next pair in the given relation. The result is R^2 = {(a, c), (b, d)}.
Step-by-step explanation:
The student asked to find R^2 for a given set A = {a, b, c, d} and a relation R = {(a, b), (b, c), (c, d)} on A x A. To find R^2, also known as the square of relation R, we need to find all the pairs (x, z) such that there exists a y in A for which (x, y) and (y, z) are in R.
R^2 is the composition of R with itself, and we calculate it by looking for pairs where the second element of one pair is the first element of another pair in R. Doing this for our given R, we get:
- (a, c): Since (a, b) and (b, c) are in R.
- (b, d): Since (b, c) and (c, d) are in R.
Therefore, R^2 = {(a, c), (b, d)}.